The maximum a posteriori (MAP) algorithm provides the optimum performance for MIMO detection. However, the MAP algorithm has high complexity, which makes it unacceptable in practical cases. Even though some simplified versions are proposed, e.g. max-log MAP (MLM), they still suffer from high complexity problem. When the a priori information is not available or the transmitted symbols are uniformly distributed, the MAP algorithm becomes the maximum likelihood (ML) algorithm. The ML is a powerful detection algorithm for multi-input multi-output (MIMO) transmission, e.g. SM transmission mode. However, it also has a high complexity especially for higher level modulation schemes such as 64-QAM, and multiple data layers, e.g. two code words transmitted simultaneously through SM transmission mode. This high complexity makes the ML detection unfeasible in practical communication systems.
In order to have a lower complexity, the conditional maximum likelihood (ML) algorithm may be considered as the detection algorithm at the receiver. In such a receiver, symbols in one layer are decoded by assuming that symbols in other layers are estimated. With this algorithm, for decoding one group of symbols, the number of distances to be calculated will be O(ML−1) instead of O(ML), where M denotes the constellation size and L corresponds to the number of symbols to be detected in one group. For example, for MIMO (2×2) transmission using SM with two code words, only 2M distances are calculated instead of M2 distance calculations.
With MIMO transmission, multiple code words are transmitted in parallel through multiple layers from multiple antennas and, consequently, a superposition of these layers arrives at receiver antennas. For the purpose of detecting the transmitted symbols, interference cancellation (IC) methods are being investigated. One of the popular approaches is the successive interference cancellation (SIC). With the SIC, symbols in different layers are detected step-by-step and the estimated interference is successively removed from the received superimposed signals. Furthermore, the SIC allows to simplify the hardware design, since equalization and decoding of different layers can utilize the same equalizer and decoder one after another. This SIC principle has been integrated with different equalization algorithms resulting in different SIC methods. Most popular ones are minimum mean square error (MMSE) equalizer based SIC (MMSE-SIC) and zero forcing (ZF) equalizer based SIC (ZF-SIC). The SIC is even investigated for MLM detector and it is named MLM-SIC.
The SIC detection improves system performances remarkably, especially the MLM-SIC method. However, the SIC method always needs to decide which layer should be decoded first and which one should be followed. The performance of SIC is seriously impacted by this order. In order to obtain an appropriate order, a special module sorting all layers is indispensable, resulting in more calculation efforts. Based on some criteria, the calculation efforts can be remarkable.
In recent years, with the appearance of “turbo principle”, iterative receivers are becoming more and more popular and promising because of their attractive performances. Different mechanisms have already been proposed and studied. The IC process can also benefit from the “turbo principle”. For example, based on MLM-SIC, the Iterative MLM-SIC is proposed. The Iterative MLM-SIC utilizes “soft” information from channel decoder instead of hard decision used by MLM-SIC. With this Iterative MLM-SIC, system performances are improved. However, the order of decoding is still needed. The Iterative MMSE-IC has also been proposed and investigated. It can provide ML like performance; however, the equalizer coefficients have to be updated at each iteration, resulting in a very high complexity. Even though some simplified versions have been proposed, they come with performance degradation.
Thus there is a need for proposing less complex and more efficient decoding process.